Highly-flexible wide angle of incidence terahertz metamaterial absorber

a r X i v :0808.2416v 2 [c o n d -m a t .m t r l -s c i ] 18 A u g 2008Highly-?exible wide angle of incidence terahertz metamaterial

absorber

Hu Tao,1C.M.Bingham,2A.C.Strikwerda,3D.Pilon,3D.Shrekenhamer,2

https://www.sodocs.net/doc/dc2863667.html,ndy,2K.Fan,1X.Zhang,1,?W.J.Padilla,2and R.D.Averitt 3,?1Boston University,Department of Manufacturing Engineering,15Saint Mary’s Street,Brookline,Massachusetts,024462Boston College,Department of Physics,140Commonwealth Ave.,Chestnut Hill,MA 024673Boston University,Department of Physics,590Commonwealth Ave,Boston,Massachusetts,02215(Dated:August 18,2008;Received)Abstract We present the design,fabrication,and characterization of a metamaterial absorber which is resonant at terahertz frequencies.We experimentally demonstrate an absorptivity of 0.97at 1.6terahertz.Importantly,this free-standing absorber is only 16microns thick resulting in a highly ?exible material that,further,operates over a wide range of angles of incidence for both transverse electric and transverse magnetic radiation.

The initial impetus driving metamaterials research was the realization that a negative refractive index n(ω)=

μ(ω)/?(ω)in a manner not easily achieved with naturally occurring materials.This new-found approach to engineering n(ω)and Z(ω)o?ers unprecedented opportunities to realize novel electromagnetic responses from the microwave through the visible.This includes cloaks,concentrators,modulators,spoof plasmons,with many more examples certain to be discovered in the coming years[4,5,6,7,8,9].

Quite recently,there has been considerable interest in creating resonant metamaterial absorbers which,through judicious design of n(ω)and Z(ω),o?er the potential for near unity absorption[10,11,12].The idea is to minimize the transmission and to simultane-ously minimize,through impedance matching,the re?ectivity.This has been experimen-tally demonstrated at microwave and terahertz frequencies[10,11,12].Recently,other approaches have been theoretically put forward to extend these ideas to higher frequencies or to increase range of angles of incidence over which the absorptivity remains su?ciently large for applications[13,14,15].

While the idea of designing a resonant absorber could be of potential use throughout the electromagnetic spectrum,this concept is expected to be especially fruitful at terahertz frequencies where it is di?cult to?nd strong absorbers.Such absorbers would clearly be of use for thermal detectors or as a coating material to mitigate spurious re?ections using continuous wave sources such as quantum cascade lasers[10,11,16,17].Progress has been promising where the initial design yielded an absorptivity of0.70at1.3THz[11].This work has been extended to a polarization insensitive design with a demonstrated absorptivity of 0.65at1.15THz[12].

In this letter,we experimentally demonstrate a resonant metamaterial with an absorp-tivity of0.97at1.6THz.In comparison to previous designs[11,12],the current design has several important advantages.Most importantly,the present design is on a freestanding highly-?exible polyimide substrate8μm thick which enables its use in nonplanar applica-tions as it can easily be wrapped around objects as small a6mm in diameter.In addition, we demonstrate,through simulation and experiment,that this metamaterial absorber oper-ates over a very wide range of angles of incidence for transverse electric(TE)and transverse

FIG.1:THz metamaterial absorber consisting of two metallic layers and two dielectric layers.

(a)Electric SRR:unit cell a:36μm,SRR side length b:25.9μm,capacitor length c:10.8μm, capacitor gap g:1.4μm,line width w:3μm.(b)Perspective view of the absorber.Each dielectric layer t1and t2is8μm thick.(c)Photograph of a portion of the experimentally realized absorber.

magnetic(TM)con?gurations.Finally,the bottom layer of the absorber consists of a contin-uous metal?lm which simpli?es the fabrication in that,for this two layer structure,precise alignment between the layers is not required.We also discuss the relative importance of losses in the metal and dielectric spacer layer.

Maximizing the absorption A is equivalent to minimizing both the transmission T and re-?ectivity R in that A=1-T-R.As has been demonstrated[12],in the limit that impedance matching to free space is achieved(i.e.Z=Z o resulting in R=0),the transmission reduces to T=exp(-2n2dk)=exp(-αd)where k is the free space wave vector,d is the sample thick-ness,n2is the imaginary part of the refractive index,andαis the absorption coe?cient. Thus,impedance matching is a crucial step yielding a transmission that is determined solely by the losses in the slab of thickness d.In the case of a metamaterial absorber the e?ective n2is determined by?(ω)andμ(ω).Thus,the design of a near-unity resonant metamaterial absorber,?(ω)andμ(ω)must be optimized such that,at the desired center frequency,Z= Z o with n2as large as possible.

A compact metamaterial absorber consists of two metallic layers separated by a dielectric spacer.The top layer consists of an array of split ring resonators which is primarily respon-sible for determining?(ω)while the bottom metallic layer is designed such that the incident magnetic?eld drives a circulating currents between the two layers.However,given the strong coupling between the two layers,?ne tuning of the geometry is required to obtain the conditions described in the previous paragraph.Fortunately,using full-wave electromagnetic simulation,rapid convergence to a near optimal design is readily achieved.

Figure1presents such an optimized design which we have subsequently fabricated and tested.The top layer(Fig.1(a))consists of an array of200nm thick Au electrically resonant split ring resonators[18,19],with the dimensions as listed in the?gure caption. In the absence of a second metallic layer,this structure yields a pure?(ω)response,and can be thought of as an LC circuit as described elsewhere[18,19].A dielectric spacer layer8μm thick separates the top and bottom metallic layers.The bottom metallic layer is a continuous200nm thick Au?lm.As Figure1(b)shows,there is a second8μm thick dielectric layer which provides mechanical support but,being behind the continuous Au ?lm,does not contribute to the electromagnetic response.Figure1(c)shows a photograph of a portion of the structure we have fabricated and tested as detailed below.

The optimized structure presented in Figure1was obtained through computer simulations using the commercial program CST Microwave Studio T M2006B.04.The frequency domain solver was utilized where the Au portions of the metamaterial absorber was modeled as lossy gold with a frequency independent conductivityσ=4.09×107S/cm.The8μm thick dielectric layer was modeled using the experimentally measured value of polyimide as this is what is used in the subsequent fabrication.Speci?cally,a frequency independent?=?1+i?2 =2.88+i0.09was used which corresponds to a loss tangent tan(δ)=?2/?1=0.0313[20].The amplitude of the transmission S21and re?ection S11were obtained and the absorption was calculated using A=1-R-T=1-S211-S221where,as expected for the present design,S21is zero across the entire frequency range due to the ground plane.The optimized structure presented in Fig.1was obtained(simulating radiation at normal incidence)through parameter sweeps of the dimensions of the SRR and the dielectric spacer thickness.The optimized parameters are those which yielded the lowest re?ectivity at the design frequency of1.6THz.

The simulated absorption as a function of frequency for the optimized structure(Fig.1) is presented in Figure2for TE(Fig.2(a))and TM(Fig.2(b))radiation at various angles

FIG.2:Simulations of the metamaterial absorber showing the absorptivity as a function of fre-quency at various angles of incidence for(a)TE and(b)TM incident radiation.The insets depict the orientation of the?elds with respect to the SRR.The labels for the curves show the angle of incidence and the corresponding peak absorptivity.

of incidence.For the TE case,at normal incidence a peak absorption of0.999is obtained. With increasing angle of incidence,the absorption remains quite large and is at0.89at50o. Beyond this there is a monotonic decrease in the absorption as the incident magnetic?eld can no longer e?ciently drive circulating currents between the two metallic layers.There is also a slight frequency shift of～30GHz from0o to80o.For the case of TM radiation shown in Fig.2(b),the absorption at normal incidence is0.999at normal incidence and remains greater than0.99for all angles of incidence.In this case,the magnetic?eld can e?ciently drive the circulating currents at all angles of incidence which is important to maintain impedance matching.The frequency shift for TM radiation is～80GHz from0o to80o.As these simulations reveal,this MM absorber operates quite well for both TE and TM radiation over a large range of angles of incidence.

An additional aspect to consider in the design of metamaterial absorbers are losses in

the constituent materials comprising the structure.As discussed in the introduction,one of the design criteria is to obtain a large value of the imaginary part of the e?ective refractive index.This necessitates having some losses in the metal.Losses in the dielectric spacer are expected to contribute as well.For example,in the limit of a perfect electric conductor and a lossless dielectric,the absorption in the composite in Fig.1is zero.However,losses in gold are su?cient to yield a strong narrow band resonance as shown in Figure2.

Fig.3(a)and(b)show the calculated surface current density for a TE wave at resonance. The currents are in opposite directions on SRR and the ground plane as expected for a magnetic resonance.Figure3(c)shows the absorption as a function of frequency for the design in Fig.1.The black curve assumes a lossless dielectric-i.e.tan(δ)=0.In this case, the peak absorption is0.88which is smaller than the calculations in Figure2.This suggests losses in the dielectric contribute to increasing the absorption.For example,increasing tan(δ)to0.04(blue curve,Fig.3(c))increases the absorption to0.99which is an increase of 0.11in comparison to a lossless dielectric.However,a point of diminishing return is reached for larger values of tan(δ)(see Fig.3(c))in that the absorption decreases and the resonance broadens.These results suggest that optimization of tan(δ)of the dielectric spacer can maximize the metamaterial absorption.Further,it appears the losses in polyimide(tan(δ) =0.0313)should contribute～0.1to the absorption of our metamaterial absorber as is evident by comparing the black curves in Fig.2(a)and3(c).

The free standing absorber structures were fabricated with a surface micromachining process on?exible polyimide substrate using a silicon wafer as the supporting substrate during the fabrication process.Liquid polyimide(PI-5878G,HD MicroSystems T M)was spin-coated on a2inch silicon wafer to form the free standing substrate.In this work, the polyimide was spin-coated at1,700rpm and cured for?ve hours in an oven at350C in a nitrogen environment yielding an8μm thick polyimide layer.A200nm thick Au/Ti ?lm was e-beam evaporated on the polyimide substrate to form the ground plane.Another 8μm thick polyimide layer was spin coated on the top of the ground plane to form the polyimide spacer and processed according to the procedure mentioned above.For the SRR array,direct laser writing technology was chosen over traditional mask contact lithography technology to improve the patterning quality on the polyimide substrates.Shipley T M S1813 positive photoresist was?rst calibrated and then exposed with a HeidelbergTM DWL66 laser writer to pattern the top layer of electric ring resonators.Another200nm thick

FIG.3:(a)and(b)show the simulated on-resonance surface current density on the SRR and ground plane,respectively,for TE incident radiation.The currents are oppositely directed as expected for a magnetic resonance.(c)Simulation of the absorption as a function of frequency for various values of the dielectric loss tangent.The curves are labeled with the value of tan(δ)used in the simulation.

Au/Ti?lm was e-beam evaporated followed by rinsing in acetone for several minutes.The metamaterial absorber fabricated on the polyimide substrate was carefully peeled o?of the silicon substrate at the end of fabrication.Our samples show great mechanical?exibility and can be easily wrapped around a cylinder with a radius of a few millimeters.

A Fourier transform infrared(FTIR)spectrometer was used to experimentally verify the behavior of the absorber by measuring the transmission and re?ection over the frequency range of0.6THz to3THz with a resolution of15GHz.A liquid helium cooled bolometer detector and6μm mylar beam splitter were used to optimize the FTIR performance over the frequencies measured.Prior to measurement,the free standing absorber samples were diced into1cm×1cm squares.The aperture of the incident beam was5mm,which is considerably smaller than the sample dimension.The sample was mounted at normal incidence for the transmission measurement.As expected,the transmitted intensity was essentially zero due to the gold ground plane which blocks all radiation through the absorber.

FIG.4:Experimentally measured absorption as a function of frequency for(a)TE and(b)TM radiation at30o,45o,and60o angles of incidence.

The achievable incident angle for re?ection measurements is constrained within the range from30to60o?-normal due to the experimental limitations.The measurements were performed with electric?eld perpendicular to the SRR gap to excite the electric resonance. The absorption spectrum was easily obtained from the re?ection results(i.e.A=1-R).

The experimental results are displayed in Figure4(a)and(b)for TE and TM incident radiation,respectively.For the TE radiation,the absorption peaks at0.95for an angle of incidence of30o decreasing slightly to0.88at60o.This is in reasonable agreement with the simulations though the experimental absorptivity at60o is～0.09higher than for simulation.However,the o?-resonance absorptivity is quite large in disagreement with the simulations.This may arise,in part,from scattering of radiation from imperfections arising from the fabrication.For the TM measurements the peak absorptivity is0.968at30o angle of incidence and only drops by0.024upon increasing to60o.Further,the increase in the baseline absorption is much smaller in comparison to the TE measurements and is in better agreement with simulations.A closer inspection of Fig.4(b)also reveals a slight increase

in the resonance frequency with increasing angle of incidence in agreement with simulation. Overall,these results substantially con?rm the simulation results demonstrating that our MM absorber yields a large absorptivity over a broad range of angles of incidence for both TE and TM radiation.

In summary,we have presented the design,fabrication,and characterization of a highly ?exible metamaterial absorber that,experimentally,obtains an absorptivity of0.96at1.6 THz,and further,operates over wide angular range for TE and TM radiation.Such a com-posite THz metamaterial may?nd numerous applications ranging from the active element in a thermal detector to THz stealth technology.

We acknowledge partial support from the Los Alamos National Laboratory LDRD pro-gram,DOD/Army Research Laboratory W911NF-06-2-0040,NSF EECS0802036,and DARPA HR0011-08-1-0044.The authors would also like to thank the Photonics Center at Boston University for all of the technical support throughout the course of this research.

?Electronic address:xinz@https://www.sodocs.net/doc/dc2863667.html,

?Electronic address:raveritt@https://www.sodocs.net/doc/dc2863667.html,

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